Why is 0.99999999… equal to 1? This is one of those questions which always puzzled me to begin with. How on Earth…

Sets of integers with no large sum-free subset Eberhard et al, Ann. Math. 2014.

上次讀過的 Erdos 1965 年的論文裡的幾個問題其中之一，這裡有最新的結果。這裡證明了，對任何的 ε>0，都存在一個整數的子集合 A，|A|=n，讓你從 A 裡隨便取 (1/3 + ε)n 個數字，一定會遇到裡頭有 x、y、z 相異整數，讓 x+y=z…

What is the biggest whole number that you can write down or describe uniquely? Well, there isn’t one, if we allow ourselves to idealize a bit. Just write down “1”, then “2”, then… you’ll never find a last one.

Of course, in real life you’ll die before you get to any…

I know, I know, you may say I’m kind of mad or anything for stating something like that in the title of this text. Actually, if there was no asterisk at the end, we could still have a very nice…

Number parity is the grown up term for talking about whether a number is even or odd. Today we’ll take this elementary concept, define it formally and use it as a launching point to prove some basic results.

Even if I’m studying Applied Mathematics, I always had a great interest in Number Theory, it was so “simple” and “fun” for me (at least in high school -but in general it’s not that simple at all).

2 — the last digit is even (0, 2, 4, 6, 8) E.G. 128 = 64.

3 — the sum of all digits can be divisible by 3. E.G. 381 (3+8+1 = 12; 12÷3 = 4.

4 — the last 2 digits are divisible by 4. E.G. 268 (68÷4= 17）